Verify that y = log (x+√x^2+a^2) satisfies the differential equation (d^2y/dx^2)+x(dy/dx)=0.

Question

Verify that y = log (x+√(x²+a²)) satisfies the differential equation \(\cfrac{d^2y}{dx^2}+x\cfrac{dy}{dx}=0.\)

(d²y/dx²)+x(dy/dx)=0.

Answer 1

Given \(y=log(x+\sqrt{x^2+a^2})\)

On differentiating with x, we get

On differentiating again with x, we get